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Frequency diversity through hopping results in performance gain (fig. 1). Expectably, performance is better over larger delay spread channel VehB. Naturally, performance is improved as the interleaving depth is increased (fig. 2). However, the gain from employing frequency hopping as opposed to plain block interleaving is reduced. This is because the attainable frequency diversity between two time slots decreases with their time difference Δt, due to the multiplicative factor J o (2πf D Δt) in the channel correlation function. The effect of the Doppler spread depends on the channel (fig. 3). Substantial gain can be attained if only a subset of the hopping patterns is used, such that any hop is at least 20 tones (fig. 4). FH-OFDM for Mobile Broadband Wireless Access Kostas Stamatiou, John G. Proakis Abstract We are studying the deployment of Frequency Hopped OFDM (FH-OFDM) at the downlink of a cellular mobile radio system. Each user in a cell is assigned a number of tones by the base- station, which change over time according to a predetermined hopping pattern. The construction of the hopping patterns is based on orthogonal latin squares, which have desirable properties regarding intra-cell interference avoidance and inter- cell interference averaging. In this work, the performance in terms of the bit-error-probability is evaluated analytically for two coded modulation schemes, i.e. TCM and BICM, combined with a block interleaver, without taking into account the adjacent cell interference. Our objective is to quantify the effect of the channel parameters, the hopping pattern selection and the interleaver depth on the performance of a coded FH-OFDM link. Motivation OFDM Orthogonal multiple access: No intra-cell interference (potential for higher capacity than CDMA) High data rates without the need for equalization (simple receiver design) Frequency Hopping Frequency diversity (gain through coding) Inter-cell interference averaging (higher frequency reuse) Candidate technology for FH-OFDM Downlink Each mobile is assigned a number of tones, according to its demand in bandwidth The tones change over time according to a hopping pattern MS 2BS MS f t Bandwidth OFDM symbol Interference Different hopping patterns are assigned to adjacent cells in order to average inter-cell interference Cell 1Cell 2 Parameters Carrier frequency2 GHz Bandwidth1.25 MHz OFDM symbol duration, T s 100 μsec Cyclic prefix duration, T cp ~ 11,1 μsec Tone spacing, 1/T11.25 KHz FFT size, N128 Number of tones used, N113 Period of hopping sequences 113 T cp T TsTs t OFDM symbol Channel Model Channel impulse / frequency response: where g k (t) are WSS, independent, CN (0,2σ k 2 ) Jakes model for each tap (f D is the Doppler frequency) Correlation function: Noise is AWGN Vehicular Test Environments UMTS macro-cellular channel model also considered for Vehicular Test Environments (TE) VehA and VehB Latin Squares For α = 1,…,N-1 define an NxN matrix A α by setting A α (i,j) = αi + j (modN) where i,j = 0,…,N-1 and N is a prime number. The set {A α } is a family of N-1 mutually orthogonal latin squares. Example: N = Cell A Cell A 2 Properties The rows and columns of A α represent the OFDM tones and time slots respectively If an element of A α is assigned to a user, a N-periodic hopping pattern is constructed for that user Hopping patterns within cell are orthogonal There can be only one collision between any pair of hopping patterns in two different cells (interference randomization) Δf between two consecutive tones in the hopping pattern of any user in cell A α is either -(α -1 )modN or N-(α -1 )modN TCM Base-station with Trellis Coded Modulation (TCM ) TCM Encoder TCM Encoder Block Symbol Interleaver (depth β) Block Symbol Interleaver (depth β) Hopping pattern generator Hopping pattern generator Coded streams of other users Symbol mapper Symbol mapper One tone/user/OFDM symbol Latin squares, N = 113 Rate 2/3, 8-state Ungerboeck code with 8-PSK (L min = 2) OFDM Mod. Binary Source Binary Source Performance - TCM The bit-error-probability is approximated by where E is the set of dominant error events (L 3, S = 4) is the number of bit errors for the symbol error event e (obtained from code error-state-diagram) H is the hopping pattern event of span S Perfect channel estimation Block interleaver span α >> S BICM Rate 1/2, 8-state Convolutional Code with 16-QAM Higher diversity order (d free = 4), but half the trellis complexity Same information rate (20kbps) Conv. Encoder Conv. Encoder Binary Source Binary Source Block Bit Interleaver (depth β b ) Block Bit Interleaver (depth β b ) OFDM Mod. Hopping pattern generator Hopping pattern generator Coded streams of other users Gray mapper Gray mapper Bit-interleaving and Gray mapping c1c1 c2c2 c3c3 cαcα c α+1 c α+2 c α+3 c 2α c (β-1)α+1 c (β-1)α+2 c βα c (β-1)α+2 c 2α+1 c 2α+2 c 2α+3 c 3α c 3α+1 c 3α+2 c 3α+3 c 4α 16-QAM symbol x 1 α βbβb 16-QAM symbol x d min αβ b = codeword length α >> d free Performance - BICM The bit-error-probability is approximated by the expression where P(d free |H) is the probability of the only minimum distance binary error event ( ), for given hopping pattern event H Generally a very complicated problem to compute P(d free |H) (very complex metrics) Simplification: For high SNR, probability of erroneous decision on a bit transmitted in symbol x k is dominated by the closest neighbor of x k with the complementary bit This neighbor is unique for Gray mapping Results - TCM Base-station with Bit-interleaved Coded Modulation (BICM) Results - BICM Fig. 1 – TCM performanceFig. 2 – Effect of interleaving Fig. 3 – Effect of Doppler spreadFig. 4 – Effect of hopping pattern selection Conclusions - TCM Conclusions - BICM The BICM scheme outperforms the TCM one (fig. 5), since the diversity order of the convolutional code (d free = 4) is higher than the diversity order of the Ungerboeck code (L min = 2, which is the minimum symbol error event length). Moreover, while the information rate achieved by both schemes is 2 bits/symbol, the trellis complexity of BICM is half that of TCM. Increasing the interleaver depth leads to greater performance gain than in the TCM case (fig. 5). Inversely, frequency hopping as opposed to plain block interleaving also provides more significant gain for BICM compared to TCM (compare fig. 6 and fig. 1,2). The above observations are related to the fact that the higher the diversity order of a code, the more difficult it is for it to be acquired for a given degree of channel correlation. Additional time or frequency diversity thus leads to greater performance gain, as the diversity order of the code is increased. Future work Consider a multi-cellular system with frequency re-use factor 1 Effect of interference randomization on the outage capacity Deployment of MIMO techniques to increase data rate, increase diversity and suppress the interference Imperfect channel estimation Iterative decoding (e.g. LDPC) Fig. 5 – Comparison of BICM and TCMFig. 6 – Effect of frequency hopping on BICM performance

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